@article{article_616325, title={On the geometry of fixed points of self-mappings on S-metric spaces}, journal={Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, volume={69}, pages={1184–1192}, year={2020}, DOI={10.31801/cfsuasmas.616325}, url={https://izlik.org/JA82KY55ES}, author={Özgür, Nihal and Taş, Nihal}, keywords={$S$-metric space, fixed circle, $S$-Pata type $x_{0}$-mapping, $S$-Pata Zamfirescu type $x_{0}$-mapping}, abstract={<p>In this paper, we focus on some geometric properties related to the set Fix(T), the set of all fixed points of a mapping T:X→X, on an S-metric space (X,S). For this purpose, we present the notions of an S-Pata type x₀-mapping and an S-Pata Zamfirescu type x₀-mapping. Using these notions, we propose new solutions to the fixed circle (resp. fixed disc) problem. Also, we give some illustrative examples of our main results.  <span style="font-size:12px;">In this paper, we give new solutions to the fixed circle (resp. fixed disc) problem on S-metric spaces. In Section 2, we prove some fixed circle and fixed disc results  </span> <span style="font-size:12px;">using different approaches. In Section 3, we give some illustrative examples of our obtained results and deduce some important remarks. In Section 4, we summarize  </span> <span style="font-size:12px;">our study and recommend some future works. </span> </p>}, number={2}, organization={Balikesir University}